While minimizing external regret is only guaranteed to converge to the set of Nash equilibria for two-player zero-sum games, researchers have found that in practice, it often also approximates the Nash equilibria of zero-sum games with larger number of players [1]}, [2]}. Given that greedy weights can significantly speed up regret minimization in such games, we ask the natural question of whether it can be used to approximate the Nash equilibria of zero-sum games with 3 or more players by speeding up external regret minimization. Figure REF  shows our results for randomly generated games with between 2 and 5 players. In two-player zero-sum games, exploitability and regret move down in lockstep, but in games with three or more players, the two measures diverge. Nevertheless, greedy weights sometimes finds approximate Nash equilibria with lower exploitability, though the gain is not nearly as large as the gains in minimizing external regret.
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